Found the problem. I had used the supplier ID from the previous application as the "External ID" column during import. Most of the records had a value, but some did not. Those that were "empty" (they actually contained spaces) were simply skipped by the import. However, once I opened the .csv file in OpenOffice, filtered on the External ID column (where value begins with " "), and deleted all content from the "empty" cells, then I was able to import all of the records, including the External IDs.

I have run into similar problems with "blank" cells in other imports. Doing a "delete all" on those cells sometimes gets rid of import (validation) errors. It seems like any error message that appears is often misleading. When importing products, the validator complained that none of the records contained a product_id, though the column was clearly present. Turns out there were a couple of blanks, and the "delete all" trick (or removal of the entire row) allowed the import to proceed.